Developments in Ceramic Materials Research

120
José M. Rojo, José L. Mesa and Teófilo Rojo
Figure 18. Specific heats (Cp) of (a) Mo(PO 3) 3 and (b) Fe(PO 3) 3. Cl and Cm are the estimated lattice
and magnetic contributions, respectively. The nsets show the heat capacity of Mo(PO 3) 3 and Fe(PO 3) 3
in the neighbourhood of the ordering temperature. The solid lines correspond to the T T N
equations.
The specific-heat data of these three metaphosphates have been fitted in the 10-25 K
temperature range with the law Cp = AT 3 + BT -2 , which assumes a Debye model (AT 3 ) for the
phonons and a BT -2 term for two-dimensional magnetic correlations (see Table 3).
The increase of Cp above 15 K is mainly due to the lattice vibrations which are given by
the A values being similar in the three metaphosphates studied (see Table 3). The contribution
of short-range 2D magnetic interactions, expected to give rise to a Schottky-type anomaly
above TN, associated with the B constant is practically neglected being significantly lower in
the chromium than in the molybdenum and iron phases.
The specific-heat data for all the three metaphosphates, at temperatures higher than 10 K,
have been fitted to the relationship Cp= AT 3 + BT -2 , where the first term is ascribed to the
lattice contributions whereas the second one deals with the 2D magnetic correlations
(Schottky tail). A linear plot of CT 2 vs. T 5 allowed the evaluation of the A= 3.05x10-4 JK -
4 mol and B= 73.5 KJmol -1 constants for chromium; A= 5.22x10 -4 JK -4 mol and B= 273 KJmol -
1 for the molybdenum and A= 4.33x10 -4 JK -4 mol and B= 278 JKmol -1 for the iron
metaphosphate. The A values are related to the Debye temperatures (θD), given in Table 3, in
the framework of the Debye model for all the metaphosphates studied. We used the inferred
value of A to substract the lattice contribution from the measured specific heat in order to
obtain the experimental magnetic specific heats (see insets Figures 17 and 18). The absence
of appreciable anomalies in the magnetic heat-capacity obtained above TN suggests that shortrange
orders would be small without any significant in the magnetic behavior of both
compounds. These results are in good agreement with those obtained from the susceptibility
measurements where decrease in the χmT vs. T curves, from 3.64 μB at room temperature to